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What is the point slope form?
What is the slope intercept form?
Define the difference of cubes.
xÂ³  yÂ³ = (x  y)(xÂ² + xy + yÂ²)
Define the sum of cubes.
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What is the quadratic formula?
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What is the standard form of a quadratic equation?
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What is the standard form for the equation of a circle?
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Define the difference of squares.
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What is the representation of imaginary numbers?
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Define the distance formula.
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What is the midpoint formula?
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What condition must hold for a graph to be symmetric with respect to the xaxis?
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What condition must hold for a graph to be symmetric with respect to the yaxis?
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What condition must hold for a graph to be symmetric with respect to the origin?
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Define completing the square.
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What is the formula for the slope of a line passing through two points?
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What condition indicates that two lines are parallel?
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What condition indicates that two lines are perpendicular?
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Define an even function.
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Define an odd function.
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What is the greatest integer function?
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What is a vertical shift upward in terms of a function?
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What is a vertical shift downward in terms of a function?
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What is a horizontal shift to the right in terms of a function?
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What is a horizontal shift to the left in terms of a function?
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What represents a reflection in the xaxis?
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What represents a reflection in the yaxis?
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How is the sum of two functions represented?
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How is the difference of two functions represented?
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How is the product of two functions represented?
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How is the quotient of two functions represented?
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How is the composition of two functions represented?
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Study Notes
Algebra II Formulas

Point Slope Form:
Useful for writing the equation of a line given a point ((x_1, y_1)) and the slope (m). Formula: (y  y_1 = m(x  x_1)). 
Slope Intercept Form:
Represents linear equations, where (m) is the slope and (b) the yintercept. Formula: (y = mx + b). 
Difference of Cubes:
A polynomial identity used to factor the difference of two cubes. Formula: (x^3  y^3 = (x  y)(x^2 + xy + y^2)). 
Sum of Cubes:
A polynomial identity for factoring the sum of two cubes. Formula: (x^3 + y^3 = (x + y)(x^2  xy + y^2)). 
Quadratic Formula:
Used to find the roots of a quadratic equation (ax^2 + bx + c = 0). Formula: (x = \frac{b \pm \sqrt{b^2  4ac}}{2a}). 
Quadratic Equation:
A seconddegree polynomial equation expressed as (ax^2 + bx + c = 0). 
Standard Form for Equation of a Circle:
Represents a circle's equation, where ((m,n)) is the center and (r) is the radius. Formula: ((x  m)^2 + (y  n)^2 = r^2). 
Difference of Squares:
A factoring identity for the difference of two squares. Formula: (x^2  y^2 = (x + y)(x  y)). 
Imaginary Numbers:
Defined by the square root of negative one, represented as (i), where (i = \sqrt{1}). 
Sum of Squares:
Representation involving squares of numbers, though it cannot be factored into real numbers. Formula: (x^2 + y^2 = (x^2 + xy + y^2)). 
Distance Formula:
Used to calculate the distance (d) between two points ((x_1, y_1)) and ((x_2, y_2)). Formula: (d = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2}). 
Midpoint Formula:
Determines the midpoint between two points. Formula: (\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)). 
Symmetry in Graphs:
 Xaxis: A graph is symmetric with respect to the xaxis when ((x, y)) corresponds to ((x, y)).
 Yaxis: Symmetry around the yaxis occurs when ((x, y)) corresponds to ((x, y)).
 Origin: Symmetry about the origin is present when ((x, y)) corresponds to ((x, y)).

Completing the Square:
A method to transform quadratic equations into vertex form. Formula: (x^2 + bx + \left(\frac{b}{2}\right)^2 = \left(x + \frac{b}{2}\right)^2). 
Principal Square Root of a Number:
For a negative number (a), the square root is defined in terms of imaginary numbers. Formula: (\sqrt{a} = \sqrt{ai}). 
Slope of a Line:
The slope (m) of a line passing through two points can be calculated. Formula: (m = \frac{y_2  y_1}{x_2  x_1}). 
Parallel Lines:
Two lines are parallel if their slopes are equal, represented as (m_1 = m_2). 
Perpendicular Lines:
Two lines are perpendicular if their slopes are negative reciprocals, represented as (m_1 = \frac{1}{m_2}). 
Even Function:
A function (f) is even if it satisfies (f(x) = f(x)). 
Odd Function:
A function (f) is odd if it satisfies (f(x) = f(x)). 
Greatest Integer Function:
Often referred to as the "floor function," visualized like a slanted ladder. 
Vertical Shifts:
 Upward Shift: (h(x) = f(x) + c).
 Downward Shift: (h(x) = f(x)  c).

Horizontal Shifts:
 Right Shift: (h(x) = f(x  c)).
 Left Shift: (h(x) = f(x + c)).

Reflections:
 In the xaxis: (h(x) = f(x)).
 In the yaxis: (h(x) = f(x)).

Operations on Functions:
 Sum: ((f + g)(x) = f(x) + g(x)).
 Difference: ((f  g)(x) = f(x)  g(x)).
 Product: ((fg)(x) = f(x)g(x)).
 Quotient: ((f / g)(x) = \frac{f(x)}{g(x)}).

Composition of Functions:
Describes the output when a function (g) is applied to the input of another function (f). Formula: ((f \circ g)(x) = f(g(x))).
Studying That Suits You
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Description
Test your knowledge of key Algebra II formulas with this set of flashcards. Each card presents a crucial mathematical concept, such as pointslope form and the quadratic formula, making it a perfect tool for review and practice. Strengthen your understanding of algebraic principles effectively!